Conformal relativity with hypercomplex variables
نویسنده
چکیده
Majorana’s arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a unified theory of general relativity and electroweak interactions. The method is extended to conformal space with the intention to introduce the strong interaction. It is then possible to use the wave equation, operating on representation functions of the conformal group, to describe the dynamics of matter fields. The resulting gauge groups resemble closely the gauge symmetries of Glashow–Salam–Weinberg and the standard model.
منابع مشابه
Numerical relativity with the conformal field equations
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled variables, the so-called “conformal field equations” developed by Friedrich. These equations allow to include “infinity” on a finite grid, solving regular equations, ...
متن کاملLocal distortion of M-conformal mappings
A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this work, we study the corresponding situation for solutions to Stein-Weiss systems in the (n + 1)D Euclidean space. This class of solutions coincides with the subset of monogenic quasiconformal mappings with nonvanishing hyper...
متن کاملDeformations of Hypercomplex Structures
Twistor theory shows that deformations of a hypercomplex manifold correspond to deformations of a canonically constructed holomorphic map from the twistor space of the hypercomplex manifold onto the complex projective line. Applying Horikawa's theory of deformations of maps, we calculate deformations of compact quotients and twists of the associated bundles of quaternionic manifolds. In particu...
متن کاملConformal Relativity versus Brans-Dicke and Superstring Theories
We show how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle–Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed Brans–Dicke action for ω = −3/2 (which is the border between standard scalar field an...
متن کاملGauge formulation of general relativity using conformal and spin symmetries.
The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers ...
متن کامل